Hostname: page-component-78c5997874-fbnjt Total loading time: 0 Render date: 2024-11-16T14:59:25.470Z Has data issue: false hasContentIssue false
  • English
  • Français

Rings Over Which Every Simple Module is Rationally Complete

Published online by Cambridge University Press:  20 November 2018

S. H. Brown
S. H. Brown*
Affiliation:
Auburn University, Auburn, Alabama
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

In 1958, G. D. Findlay and J. Lambek defined a relationship between three R-modules, A ≦ B(C), to mean that A ⫅ B and every R-homomorphism from A into C can be uniquely extended to an irreducible partial homomorphism from B into C. If A ≦ B(B), then B is called a rational extension of A and in [5] it is shown that every module has a maximal rational extension in its injective hull which is unique up to isomorphism. A module is called rationally complete provided it has no proper rational extension.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 25 , Issue 4 , August 1973 , pp. 693 - 701
Copyright
Copyright © Canadian Mathematical Society 1973

References

1. Courter, R., Finite direct sums of complete matrix rings over perfect completely primary rings, Can. J. Math. 21 (1969), 430–446.Google Scholar
2. Cozzens, J. H., Homological properties of the ring of differential polynomials, Bull. Amer. Math. Soc. 76 (1970), 75–78.Google Scholar
3. Faith, C., Lectures on infective modules and quotient rings, Lecture notes in Mathematics, No. 49 (Springer-Verlag, Berlin, 1967).Google Scholar
4. Feller, E. H., Properties of primary non-commutative ringst Trans. Amer. Math. Soc. 89 (1958), 79–91.Google Scholar
5. Findlay, G. D. and Lambek, J., A generalized ring of quotients. I and II, Can. Math. Bull. 1 (1958), 77–85 and 155-167.Google Scholar
6. Kaye, S., Ring theoretic properties of matrix rings, Can. Math. Bull. 10 (1967), 364–374.Google Scholar
7. Koh, K., On the annihilators of the infective hull of a module, Can. Math. Bull. 12 (1969), 858–860.Google Scholar
8. Rosenberg, A. and Zelinsky, D., On the finiteness of the infective hull, Math. Z. 70 (1959), 372–380.Google Scholar
9. Waddell, M. C., Properties of regular rings, Duke Math. J. 19 (1952), 623–627.Google Scholar